21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Nadin Stahn, Wed, 16.00-16.30 Previous Contents Next  
  Robust Multigrid Method for the Efficient Solution of PDEs on Complicated Domains
Nadin Stahn (Univ. Zürich)

The finite element discretisation of elliptic boundary value problems on complicated domains often results in a huge number of unknowns. Multigrid methods have the potential to solve the arising systems of linear equations in linear complexity with respect to the number of unknowns.

We employ overlapping composite finite elements for the construction of a sequence of coarse-level discretisations setting up a multigrid algorithm. The convergence of this algorithm is proved in the framework of geometric multigrid methods. The idea is to adapt the general convergence theory to the specific situation and to prove the so-called smoothing and approximation property. The emphasis is on the robustness with respect to the possibly degenerate geometry of the intersection of overlapping triangles with the domain. As a consequence the matrix entries which correspond to nodes lying (essentially) outside the domain have a very different scaling compared to those entries corresponding to interior nodes. We will study the influence of this scaling effects on the convergence rate of a multigrid algorithm for a 2d model problem.

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Last updated:
28.01.2005 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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